Simplify Square Root of 28026

Here we will show you two methods that you can use to simplify the square root of 28026. In other words, we will show you how to find the square root of 28026 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√28026 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 28026 to simplify the square root of 28026. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 28026. The factors of 28026 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 173, 346, 519, 1038, 1557, 3114, 4671, 9342, 14013, and 28026. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 28026 divided by the greatest perfect square from the list of all factors of 28026. We determined above that the greatest perfect square from the list of all factors of 28026 is 81. Furthermore, 28026 divided by 81 is 346, therefore B equals 346.

Now we have A and B and can get our answer to 28026 in its simplest radical form as follows:

√28026 = A√B

√28026 = 9√346

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 28026 to simplify the square root of 28026 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 28026 and then take the square root of that product. The prime factors that multiply together to make 28026 are 2 x 3 x 3 x 3 x 3 x 173. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 28026 by the number (A) squared. 9 squared is 81 and 28026 divided by 81 is 346. Therefore, B equals 346.

Once again we have A and B and can get our answer to 28026 in its simplest radical form as follows:

√28026 = A√B

√28026 = 9√346

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 28027
Here is the next square root on our list that we have simplifed for you.